How to make grass respond to an object hitting them
Final:



Overview:

Whole process is very easy. You will only need to make your grass object as Cloth or Soft Body (with Weight Paint) then Convert Particle System to mesh and delete Particle Emitter as it will not longer be needed. Then add to your Cube Collision.

First of all you will need to choose if you want to use Cloth or Soft Body. Quick test shows me that Cloth simulation is fairly faster, but Soft Body will give you probably more options, as Plastics, Edge Stiffness and such.

Secondly I don't know why (and maybe someone can correct me) when your object is in Particle System simulation works, but Pinning/Soft Body Goal won't. Maybe it's a bug or maybe there is an explanation.


  Note: Below steps could vary from your scene setup so don't take them
  as granted. I will point out most important settings and you could
  tweak them for your needs.


Steps:

Grass strand.




You will need to Weight Paint your grass strand. Red is stiff, green is... less stiff. You can experiment with this as you like to make grass really soft or hard.
Add to your object Cloth Simulation. I have used settings as you can see on the image. Most important things here are:


Mass - it should be really low, higher will make grass to lay on the ground,
Pinning - from Weight Paint, it will keep grass strong at the bottom and weak at the top, or not if you painted it differently, 
Velocity - how fast grass will return to base position,
Cloth Collision - check also Self Collision, there are lots of them so it will make simulation more realistic.



Particle Emitter.

Nothing special here, only after setting your grass go to Modifier Tab and Convert Particles then delete Particle Emitter.

Blend file: